In this topic you will learn about functions. You did functions in grade 9 and grade 10. In the previous classes we defined functions as the mathematical building blocks for designing machines, predicting natural disasters, curing diseases, understanding world economies and for keeping aeroplanes in the air.
In the concept of functions, we study about three types of functions; parabola, hyperbola, and exponential function. Today's lesson is about parabola. We did parabola in grade 10;
- The general formula of the mother graph is y = ax^2 + q
- When a > 0 the graph concave up
- Wgen a < 0 the graph concave down
- q is the y intercept
- Given y = x^2
- This is the mother graph
- y intercept = 0
- x intercept = 0
- Coordinates of the turning point (0 ; 0)
After this lesson you, grade 11s will be required to be able to calculate y intercept, x intercepts and the coordinates of the turning point. You have to go through the videos uploaded to have more understanding about the lesson before completing the activity. You have to be able to find the equation of parabola. When given the equation you must be able to sketch the graph of parabola.
You have to understand three general equations of parabola.
- y = ax^2 + bx + c, (i) where c is the y intercept, (ii)the graph has an axis of symmetry at x = -b/2a, (iii) function has one turning point given by (-b/2a ; f(-b/2a)), (iv) the function may have either a maximum or minimum value but not both,
- y = a(x - p)^2 + q, where p and q are the coordinates of the turning point (p ; q)
- y = a(x - x1)(x - x2), where x1 and x2 are two x intercepts
To sketch the graph of parabola, follow the following steps;
- Write down y intercept (let x =0)
- Calculate x intercepts
- Write the equation in the form ax^2 + bx + c = 0
- factorise left hand side of the equation
- Use the fact that if (x - x1)(x - x2) = 0 the x = p and x2 =q, to calculate x intercepts
- Determine axis of symmetry
- Substitute the x value of axis of symmetry to the original equation and find y value to calculate the coordinates of the turning point
- Plot the points and the draw the function using free hand
The given activity will be out of, and you will be required to calcute y intercepts, x intercepts, axis of symmetry, and the coordinates of the turning point.
You have to watch videos and go through notes and sketch the graph given the equation and find the equation of a function.
Here is the rubric:
|axis of symmetry||2|
|coordinates of turning point||3|
|Sketch the graph of the function||4|
|Find the equation of the function||5|
Thank you for attending the lesson and please to the given activity.
If you did not understand this lesson, you need to go through the youtube videos before the next lesson.
This lesson is the introduction of functions and it upfold everything about the topic.